I had a shop do a gear install a couple months ago and everything was pretty good until I started getting really bad vibrations at 80mph and up. I was looking at the bill and noticed they didn't put in the additive so called them and asked why and they said since they used royal purple it doesn't need it cause royal purple has it in the fluid. Is this alright or should they still have put the additive in?

 

You don't need to with royal purple or most of the synthetics available. If you are getting a lot of noise on slow, tight turns, then you can add a bottle of ford friction modifier. It's not going to cause a vibration if it's not in there.

They may have not put the drive shaft back exactly how it was taken out. have them unbolt it and turn it 90 degrees. I also recommend torquing in a star pattern and sneaking up on the 41 ft lbs for the drive shaft to pinion flange bolts. I always torque mine in two stages. A shop probably just hits it with an impact gun.

 

...or free hands it (no torque wrench). I'd take the car back and have them make sure everything is tight under there or have them recheck everything. You should have some sort of labor warranty for everything.

What you are describing is a driveshaft vibration. Lack of friction modifier would lead to gear chatter at low speeds and under moderate acceleration from a stop.

 

Driveshaft vibration like the others have said. Take it back. Easily fixed.